“Group Message” and “Multiple Recipient” are separate settings. They act differently.

Please let me know following
1. getting 504 when sending group message or multiple recipients (in “To” field)?
2. How many members you have in group which you are sending to?
3. Create a test group with 5/6 members and send message to that group, are you getting 504?
4. How many total messages and announcements you have?
5. Do you use any caching plugin?